THE ANALOG OF THE LIFSHITZ-KOSEVICH FORMULA FOR THE DHVA EFFECT IN THE VORTEX STATE OF A 2-DIMENSIONAL SUPERCONDUCTOR

We study the effects of the superconducting (SC) order parameter on th e magnetization oscillations in the vortex state of extremely type-II, nearly 2D superconductors. A systematic expansion of the electronic f ree energy in the SC order parameter, up to fourth order, is used to c alcuate the magnetization oscillations just below H-c2(T). An analytic al expression for the magnetization oscillations is derived. The resul ting expression is a generalization of the well known Lifshitz-Kosevic h formula, which is operative above H-c2, into the vortex state below H-c2. The expansion parameter clearly reflects the gapless nature of t he quasi-particle spectrum below H-c2. The development of the SC order parameter with the decreasing magnetic field below H-c2 generates a s ignificant contribution tot he magnetization oscillations in antiphase to the normal electrons oscillations. This seems to account for the s ignificant reduction in the dHvA amplitude observed already in several superconductors just below H-c2.